Geometry of grain boundaries
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A N a p p r e c i a t i o n of the e x i s t e n c e of an a s s o c i a t i o n b e t w e e n the g r a i n s t r u c t u r e of m e t a l s and t h e i r m e c h a n i c a l p r o p e r t i e s i s e v i d e n t in r e l a t i v e l y a n c i e n t m e t a l l u r g i c a l p r a c t i c e s . Efforts to e s t a b l i s h exact s t r u c t u r e - p r o p e r t y r e l a t i o n s h i p s have b e e n a p p e a r i n g with i n c r e a s i n g f r e q u e n c y d u r i n g the past h a l f - c e n t u r y . On the whole, these have b e e n l e s s than s a t i s f y i n g in the insight that they have p r o v i d e d toward a m o r e b a s i c u n d e r s t a n d i n g of the n a t u r e of p o l y c r y s t a l l i n e aggregates. F r o m the e x p e r i m e n t a l standpoint, d i f f i c u l t i e s a r i s e both in: 1) the s e l e c t i o n of t e s t s by which f u n d a m e n t a l a s p e c t s of the m e c h a n i c a l p r o p e r t i e s may be s e n s e d a n d in 2) the m e a s u r e m e n t and e x p r e s s i o n of the dim e n s i o n s of m i c r o s t r u c t u r e . Although t h e r e s e e m s to be a g e n e r a l a w a r e n e s s of the s h o r t c o m i n g s of the m e c h a n i c a l t e s t s and p r o c e d u r e s upon which such s t u d i e s m u s t depend, it i s evident in the l i t e r a t u r e that few i n v e s t i g a t o r s a r e c o n s c i o u s e i t h e r of the g e o m e t r i c p r i n c i p l e s that a r e a v a i l a b l e for d e a l i n g with m u l t i c e l l u l a r s t r u c t u r e s , or of the c o n s e q u e n c e s of i g n o r i n g t h e s e p r i n c i p l e s . It i s the purpose of this p a p e r to s u r v e y those r i g o r o u s l y p r o v e d g e o m e t r i c r e l a t i o n s h i p s which a r e a v a i l a b l e for the c h a r a c t e r i z a t i o n of a s t r u c t u r a l continuum of g r a i n s and for the d e f o r m a t i o n of a g r a i n b o u n d a r y network.
P A R T I)* DIMENSIONS O F T H E POLYCRYSTALLINE AGGREGATE *A condensedand reeditedversionof a manuscriptby F. N. Rhinesand J. E. Lemonsentitled"Critiqueon the Correlationof GrainSizewithPhysicalProperties" presentedat the 1967MetalsCongressin Cleveland,Ohio. A m a j o r s o u r c e of difficulty that i s m e t in a t t e m p t ing to m e a s u r e and to e x p r e s s the d i m e n s i o n s of an opaque p o l y c r y s t a l l i n e a g g r e g a t e l i e s in the c i r c u m s t a n c e that the s t r u c t u r e i s seen only a s d i s p l a y e d FREDERICK N. RHINES is Professor and Chairman of the Department of Metallurgicaland Materials Engineering,University of Florida, Gainesville,Fla. This manuscript is based on an invited talk presented at the symposium on Deformation and Strength of Polycrystals, sponsored by the IMD Physical MetallurgyCommittee, Detroit, Mich., October 14-15, 1968. METALLURGICALTRANSACTIONS
upon the s u r f a c e of a t w o - d i m e n s i o n a l section. Although knowledge of the r e l a t i o n s h i p s between r a n d o m s e c t i o
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